Empirische Prozesse

General Information

Language	German/English
Lectures	2 SWS
Excercises	1 SWS

Lectures: Wednesday 10:00 - 12:00, N24 Room 226
Excercises: Wednesday 14:00 - 16:00, Helmholtzstraße 18, Room 120
Exam s. Moodle

General Information:

Target Audience:

Master Mathematische Biometrie
Master Wirtschaftsmathematik
Master Finance
Master Mathematik

Course Prerequisites:

Elementary Probability Calculus and Statistics

Contents:

The lecture deals with modern empirical process theory. Empirical process theory started in the 1930s and 1940s with the analysis of the empirical distribution function. Back then, the main interest focused on deriving uniform convergence statements for the empirical distribution function. Modern empirical process theory deals with general uniform convergence statements, in particular, with uniform laws of large numbers (Glivenko-Cantelli theorems) and uniform central limit theorems (Donsker theorems). It is an indispensable theoretical tool for many modern fields of statistics including non- and semiparametrics, high-dimensional statistics, machine learning and biostatistics.

Literature:

A. Van der Vaart & J. Wellner (1996). Weak Convergence and Empirical Processes. Springer.
D. Pollard (1990). Empirical Processes: Theory and Applications. NSF-CBMS Regional Conference Series in Probability and Statistics: Volume 2.
G. Shorack & J. Wellner (1986). Empirical Processes with Applications to Statistics. Wiley.